Jeff holds $50,000 wealth which has a utility of 7.07 utils (assuming utility is the square root of wealth in thousand dollars).He considers investing this in a gamble which has a 0.6 probability of increasing his total wealth to $100,000 and 0.4 probability of decreasing it to $30,000.What will be Jeff's expected utility from the gamble?
A)15 utils
B)8.19 utils
C)3.2 utils
D)12.12 utils

Question

Quizplus · Accepted Answer

Jeff's expected value (EV) of the gamble is:
EV = 0.6($100,000) + 0.4($30,000) = $72,000

His expected utility (EU) from the gamble can be calculated as the weighted average of the utility of each possible outcome:
EU = 0.6(sqrt(100)) + 0.4(sqrt(30))

EU = 0.6(10) + 0.4(5.48)
EU = 9.19

Therefore, Jeff's expected utility from the gamble is 9.19 utils, which is higher than his current utility of 7.07 utils. So, Jeff should take the gamble to maximize his expected utility.

Jeff Holds $50,000 Wealth Which Has a Utility of 7